3 citations · 8 across the 10 of their papers we have counts for
10 papers
Bounds on the Mordell-Weil rank of elliptic fibrations
Antonella Grassi, Rick Miranda, Kapil Paranjape +2
We prove that the Mordell-Weil group of a higher dimensional elliptic fibration naturally embeds into that of a suitable elliptic surface. We give sufficient conditions for the exi…
Modular Forms and Calabi-Yau Varieties
Kapil Paranjape, Dinakar Ramakrishnan
Given a holomorphic newform of weight and with rational coefficients, a question of Mazur and van Straten asks if there is an associated Calabi-Yau variety over ${\math…
Quotients of E^n by A_{n+1} and Calabi-Yau manifolds
Kapil Paranjape, Dinakar Ramakrishnan
We give a simple construction, starting with any elliptic curve E, of an n-dimensional Calabi-Yau variety of Kummer type (for any n>1), by considering the quotient Y of the n-fold…
Cycles over fields of transcendence degree one
Mark Green, Philip A. Griffiths, Kapil Hari Paranjape
We extend earlier examples provided by Schoen, Nori and Bloch to show that when a surface has the property that the kernel of its Albanese map is non-zero over the field of complex…
A Geometric characterization of Arithmetic Varieties
Kapil Hari Paranjape
A result of Belyi can be stated as follows. Every curve defined over a number field can be expressed as a cover of the projective line with branch locus contained in a rigid diviso…
Higher Abel-Jacobi Maps
Jishnu Biswas, Gautham Dayal, Kapil H. Paranjape +1
This paper forms the major portion of a talk given at the International Colloquium on Arithmetic, Algebra and Geometry at TIFR, Mumbai in Jan 2000. We look at the problem of detect…